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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Differential Equations

NDA 2022 · Mathematics · Differential Equations

What is the differential equation of the family of parabolas having...

What is the differential equation of the family of parabolas having vertex at origin and axis along positive yy-axis ?

Options

  1. Axdydx+2y=0x \frac{d y}{d x}+2 y=0
  2. Bxdydx−2y=0x \frac{d y}{d x}-2 y=0
  3. Cydxdy+2x=0y \frac{d x}{d y}+2 x=0
  4. Dydxdy−2x=0y \frac{d x}{d y}-2 x=0

Correct answer

B. xdydx−2y=0x \frac{d y}{d x}-2 y=0

Step-by-step solution

Let equation of parabola is x2=4ayx^2=4 a y ...(i) ∴2x=4adydx⇒2x=x2ydydx⇒xdydx−2y=0\begin{aligned} & \therefore 2 x=4 a \frac{d y}{d x} \\ & \Rightarrow 2 x=\frac{x^2}{y} \frac{d y}{d x} \Rightarrow x \frac{d y}{d x}-2 y=0\end{aligned}
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